"Strengthening Connections with the Audience: Reformation and Exemplification in Mathematics Research Articles"

Kristy Lesperance

Kristy was in her third year of undergraduate studies at the University of British Columbia when this essay was originally written, studying Mathematics under the faculty of Arts. The paper was written for an upper-level, intensive research and scholarly writing course using corpus analysis to investigate discursive features of literature from the student’s chosen major.

Contents

Introduction

Mathematics in Discourse Analysis

Method

Results & Discussions

Results & Discussions Cont.

Conclusion

Works Cited

Results & Discussions Cont.

Code gloss markers such as this means, meaning, or we mean were used in education articles 69 percent less often than in theory articles, whereas equivalently and essentially were used solely in theory articles. On the other hand, specifically and especially were used 75 percent less often in theory than in education articles. The lexical bundle in other words was used similarly in both sub-disciplines (at about 1.4 uses per 10,000 words), but with less frequency in the present study (3.3 percent of the overall code gloss markers) than in Hyland’s study.

It is important to note that a lack of proficient understanding of the subject matter (higher level mathematics), as well as technological and time constraints in analysis, prevented the search for parenthetical reformulations as well as relevant instances of the marker which. Both of these features were significant factors in Hyland’s analysis and may therefore also appear with notable frequency in my corpus. It was noted during the present analysis that corpus articles used these reformulation markers, although not to what extent; therefore it may prove beneficial for future studies to search for these reformulations.

Exemplification – comparison across sub-disciplines

Despite the overall lower frequency of exemplification cues in the present corpus, a much broader variation in target exemplification cues was detected (52 different phrases, including 47 variations of the text surrounding example) compared with reformulation markers. As stated previously, a greater number of exemplification markers was observed in education articles (about 26 per 10,000 words) than in theory (about 14 per 10,000 words); however, a wider variety of markers was observed in theory than in education.

Both sub-disciplines tended to reuse certain markers more frequently than others, which corroborates Hyland’s finding that such as, for example, and e.g. were by far the most commonly used markers. In the present study, however, marker use varied by sub-discipline: in theory articles, 38 percent of all exemplification markers were either for example or say (with other markers used less than twice per 10,000 words); by contrast, in education, 76 percent of all exemplification markers were the same four indicators (such as, for example, like, and e.g.).

The most substantial code gloss uses in education articles were the terms such as (with 6.9 instances), for example (5.9), like, and e.g. (3.4 instances each). Significant differences were found in theory articles, however, which used such as about 87 percent less frequently than education, e.g. about 76 percent less, and like about 50 percent less. The lexical bundle an example of, although used infrequently by both sub-disciplines, was still observed about 62 percent more frequently in education articles. On the other hand, theory tended to use say about 83 percent more frequently than education, and a similar frequency was observed across both sub-disciplines in the use of counterexample(s) and for instance.

Particularly noteworthy in relation to exemplification use is the variety of phrases surrounding the code gloss marker example. Although theory used exemplification significantly less frequently than education, it did use a greater variety of phrases surrounding the word example. To be precise, 40 variations were detected (55 percent more than used by education), which included such creative forms as “one of the most interesting nonclassical examples of” and “the most important classical example of” (Bryant & Harvey, 1989, p. 1), as well as “the simplest possible example” (Monod, 2006, p. 797). In contrast, education tended to use more literal indicators of examples, in simple bundles such as an example of, in this example, and an example from.

As the present analysis focused on comparisons with Hyland’s work, some markers which did not appear in Hyland’s study were not examined closely. For example, it became apparent that there may exist unique, but commonly used, exemplification markers within mathematical discourse, such as consider, suppose, and imagine, which were not actively considered. Further research may therefore find noteworthy results by analyzing the corpus for these reformulations, or other overlooked markers, which have the potential to alter the conclusions of the present study.

Limitations and possibilities for further research

Understandably, Hyland’s comprehensive analysis reveals deeper levels of interpretation of both code gloss use and its rhetorical functions than was possible in the present study. In light of both Hyland (2007) and Cuenca and Bach (2007), exploring further levels of code gloss analysis would likely improve the saliency of the present study. Further research could also explore interdisciplinary differences in code gloss use by contrasting various mathematical topics (i.e., algebra, number theory, statistics), or by contrasting mathematics with another broadly categorized discipline (either hard or soft).

Lastly, Hyland cautions readers about accepting an author’s reformulations at face value, characterizing reformulation as “a rhetorical sleight of hand” due to its high level of subjectivity (2007, p. 277). Therefore, in further research, it might also would be interesting to investigate the level of subjectivity imbedded within reformulations by comparing reformulations of specific ideas amongst various authors.